3.8 The LLM

Stands for the linear logistic model (Maris, 1999)

Is also referred to as Compensatory Reparameterized Unified Model (CRUM)

In this model, mastering an attribute has a certain impact on the logit of the probability of success

Its IRF can be written as

$$\log \frac{P(Y_j=1|{\alpha }_{lj}^{\ast })}{P(Y_j=0|{\alpha }_{lj}^{\ast })}={\delta }_{j0}+\sum _{k=1}^{K_j^{\ast }}{\delta }_{jk}{\alpha }_{lk}$$

Please calculate probabilities based on the parameters in the graph below:

$$P[Y_j=1|{\alpha }_{lj}^{\ast }=(0,0\left)\right]=?P[Y_j=1|{\alpha }_{lj}^{\ast }=(1,0\left)\right]=?P[Y_j=1|{\alpha }_{lj}^{\ast }=(0,1\left)\right]=?P[Y_j=1|{\alpha }_{lj}^{\ast }=(1,1\left)\right]=?$$

References

Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64(2), 187–212. https://doi.org/10.1007/bf02294535